Identifying the underlying time-delayed latent causal processes in sequential data is vital for grasping temporal dynamics and making downstream reasoning. While some recent methods can robustly identify these latent causal variables, they rely on strict assumptions about the invertible generation process from latent variables to observed data. However, these assumptions are often hard to satisfy in real-world applications containing information loss. For instance, the visual perception process translates a 3D space into 2D images, or the phenomenon of persistence of vision incorporates historical data into current perceptions. To address this challenge, we establish an identifiability theory that allows for the recovery of independent latent components even when they come from a nonlinear and non-invertible mix. Using this theory as a foundation, we propose a principled approach, CaRiNG, to learn the CAusal RepresentatIon of Non-invertible Generative temporal data with identifiability guarantees. Specifically, we utilize temporal context to recover lost latent information and apply the conditions in our theory to guide the training process. Through experiments conducted on synthetic datasets, we validate that our CaRiNG method reliably identifies the causal process, even when the generation process is non-invertible. Moreover, we demonstrate that our approach considerably improves temporal understanding and reasoning in practical applications.

翻译：从序列数据中识别潜在的时间延迟因果过程，对于理解时序动态和实现下游推理至关重要。尽管现有一些方法能够稳健地识别这些潜在因果变量，但它们依赖于从潜在变量到观测数据的可逆生成过程的严格假设。然而，在包含信息损失的实际应用中，这些假设往往难以满足。例如，视觉感知过程将三维空间转换为二维图像，或视觉暂留现象将历史数据融入当前感知。为应对这一挑战，我们建立了一种可识别性理论，该理论允许恢复独立的潜在分量，即使它们来自非线性且非可逆的混合。以此理论为基础，我们提出了一种原则性方法CaRiNG，用于学习具有可识别性保证的非可逆生成时序数据的因果表征。具体而言，我们利用时序上下文来恢复丢失的潜在信息，并应用理论中的条件来指导训练过程。通过在合成数据集上进行的实验，我们验证了即使生成过程是非可逆的，我们的CaRiNG方法也能可靠地识别因果过程。此外，我们证明了该方法在实际应用中显著提升了时序理解与推理能力。